Distributed Design for Decentralized Control using Chordal Decomposition and ADMM

TL;DR

This paper introduces a distributed control design approach leveraging chordal decomposition and ADMM, enabling decentralized control synthesis with local data sharing, improving scalability and efficiency in large-scale systems.

Contribution

It develops a novel distributed control design method combining chordal decomposition and ADMM, addressing sparsity and decentralization in control problems.

Findings

Effective in decomposing large control problems

Enables local data sharing among subsystems

Numerical results confirm scalability and efficiency

Abstract

We propose a distributed design method for decentralized control by exploiting the underlying sparsity properties of the problem. Our method is based on chordal decomposition of sparse block matrices and the alternating direction method of multipliers (ADMM). We first apply a classical parameterization technique to restrict the optimal decentralized control into a convex problem that inherits the sparsity pattern of the original problem. The parameterization relies on a notion of strongly decentralized stabilization, and sufficient conditions are discussed to guarantee this notion. Then, chordal decomposition allows us to decompose the convex restriction into a problem with partially coupled constraints, and the framework of ADMM enables us to solve the decomposed problem in a distributed fashion. Consequently, the subsystems only need to share their model data with their direct neighbours, not needing a central computation. Numerical experiments demonstrate the effectiveness of the proposed method.